A gunman holding staff and customers hostage at a Lindt cafe in Sydney is referring to himself as "The Brother" and is claiming to have planted two bombs in the store and two in the city's central banking district, according to local media reports.

Australian outlet Ten Eyewitness News spoke to two of the hostages in a dramatic phone call in which they detailed information about the hostage-taker.

Correspondent Hugh Riminton tweeted: "Gunman....claims 2 bombs in #lindtcafe" and "two bombs have been placed in the CBD (central banking district)."

He added that the two women in the call were "hysterical" and believed that their lives were in "immediate danger".

He then deleted the tweets as they included the demands of the hostage-taker and Australian police requested that they not be made public by the media in order not to jeopardise the negotiations.

In a press conference, Abbott said: "Australia is a peaceful, open and generous society - nothing should ever change that and that's why I would urge all Australians today to go about their business as usual."

Six hours after the hostage situation began, three people were seen running from the cafe and two more followed an hour later.

It remains unclear whether the hostages escaped of their own accord or were released by the hostage-taker. The number of hostages left in the cafe remains unconfirmed but local media reports suggest the number is approximately 15.

"We will work with these people to figure out more information. We do not have information to suggest that anyone is harmed at this stage," said New South Wales Police Deputy Commissioner Catherine Burn.